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On statistical indistinguishability of the complete and incomplete markets

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  • Nikolai Dokuchaev

Abstract

The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market incompleteness is also non-robust: small deviations can convert an incomplete model into a complete one. More precisely, it is shown that, for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters. This leads to a counterintuitive conclusion that the incomplete markets are indistinguishable from the complete markets in the terms of the market statistics.

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  • Nikolai Dokuchaev, 2012. "On statistical indistinguishability of the complete and incomplete markets," Papers 1209.4695, arXiv.org, revised May 2013.
  • Handle: RePEc:arx:papers:1209.4695
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    References listed on IDEAS

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    Cited by:

    1. Nikolai Dokuchaev, 2015. "Modelling Possibility of Short-Term Forecasting of Market Parameters for Portfolio Selection," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 143-161, May.
    2. Nikolai Dokuchaev, 2013. "On strong binomial approximation for stochastic processes and applications for financial modelling," Papers 1311.0675, arXiv.org, revised Feb 2015.
    3. Nikolai Dokuchaev, 2015. "On statistical indistinguishability of complete and incomplete discrete time market models," Papers 1505.00638, arXiv.org.

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